Fechner’s logarithmic law is mathematically equivalent to Weber’s proportional-JND law

Evidence

Suppose we could just barely tell the difference between 10 and 11 units of light intensity, a 10% difference and an absolute difference of one unit. Weber’s prediction would be that we could also just barely tell the difference between 1 million and 1,100,000 units, a difference again of 10%, but an absolute difference of 100,000 units. In fact, Fechner called his law Weber’s law, and he was correct, because Fechner’s S = k log R implies ΔS = kΔR/R (for small changes Δ; this is proved in calculus, but can be easily checked on a calculator). So Fechner’s law is really Weber’s law, since to keep ΔS fixed at the threshold for perception, then ΔR must rise and fall as R. — Eric J. Heller, Why You Hear What You Hear- An…, 2001

Categorization

Category: Causal Relationships

• XREF: Connects to the classic Weber-Fechner derivation every psychophysics intro covers; shows the two are the same law.

Related

• Fechner’s logarithmic law and Weber’s ratio law are one and the same. (similarity 0.94)
• Sensation grows with the logarithm of stimulus strength rather than the strength itself (similarity 0.83)
• Fechner made perception measurable by tying it mathematically to physical stimuli (similarity 0.82)
• Weber’s law states JND is a constant fraction of stimulus magnitude (similarity 0.80)

Broader Connections

• Fechner made perception measurable by tying it mathematically to physical stimuli #corroborates (0.80) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 60
• The perceptual JND for weights is a constant 10 percent proportion #exemplifies (0.75) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 798